Question: Solve for $x$ : $3x^2 - 33x + 54 = 0$
Dividing both sides by $3$ gives: $ x^2 {-11}x + {18} = 0 $ The coefficient on the $x$ term is $-11$ and the constant term is $18$ , so we need to find two numbers that add up to $-11$ and multiply to $18$ The two numbers $-9$ and $-2$ satisfy both conditions: $ {-9} + {-2} = {-11} $ $ {-9} \times {-2} = {18} $ $(x {-9}) (x {-2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x -2) = 0$ $x - 9 = 0$ or $x - 2 = 0$ Thus, $x = 9$ and $x = 2$ are the solutions.